Fluctuations in the energy loss have been measured for 66- and 100-MeV protons passing through a proportional counter filled with 11.0 mg/${\mathrm{cm}}^2$ of a gas mixture of 90% xenon plus 10% methane. The measured values are consistent with the theoretical values determined from the Vavilov theory for energy-loss fluctuations; however, when the Vavilov theory is corrected for the binding effect of the electrons based on the formulation of Shulek et al., the corrected theoretical energy-loss distributions do not agree with the experimental distributions.

A Fredholm technique is used to compute elastic phase shifts for electron-hydrogen-atom scattering using the Feshbach optical potential. The method is noniterative and is computationally highly efficient as it allows computation of the Fredholm determinant $D(E+i\epsilon )$ at a series of energies from a single set of matrix elements of the optical potential. Scattering information is then obtained over a continuous range of energies by interpolation of $D(E+i\epsilon )$; resonance is easily located by inspection of the zeros of $\mathrm{Re}D(E+i\epsilon )$.

A thick Mg target was bombarded by a 21-MeV oxygen-ion beam. Nine $1s-2p$ transitions were observed with an energy resolution of 1.26 eV. Relative to the 1253.6-eV $K{\alpha }_{1,2}$ reference energy, the energies of the other observed transitions in units of eV were 1261.5, 1268.5, 1270.7, 1273.3, 1281.0, 1283.0, 1293.0, and 1295.4. By comparing with Hartree-Fock-Slater calculations, the five groups of peaks were found to correspond to $1s-2p$ ($K\alpha$) transitions with initial configurations ${\mathrm{}\left(1s\right)\mathrm{}}^{-1\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-n}$ for $n=0, 1, 2, 3, \mathrm{and} 4$. The transition for the ${\mathrm{}\left(1s\right)\mathrm{}}^{-1\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-5\mathrm{}}$ initial configuration was not observed in this experiment. This can be attributed to self-absorption in the target since the ${\mathrm{}\left(1s\right)\mathrm{}}^{-1\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-5\mathrm{}}$ $K\alpha$ transition energy lies above the $K$ absorption edge.

The proton-hydrogen charge-exchange amplitude is evaluated using the first-order terms in the Faddeev expansion for the corresponding transition operator. The new Coulomb $T$ matrix derived by us recently is employed in computing the cross sections. For high energies of the incident proton, the Coulomb $T$ matrix approaches the Coulomb potential to order $v^{-1\mathrm{}}$ $\ln v$ in contrast to the situation for a short-range potential ($\sim v^{-2\mathrm{}}$). In the extreme high-energy limit the results of the first-order Faddeev-Watson approximation approach those of the Jackson-Schiff approximation. Explicit numerical calculation in the energy region 100 keV to 3 MeV shows that the cross sections lie in between those of the Brinkman-Kramers and Jackson-Schiff (JS) results and they approach the JS results from above. This is in contradistinction to our previous work based on an incorrect form of the $T$ matrix.

The cross sections for disorientation of magnetically oriented $6{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ cesium atoms, induced in collisions with noble gases, have been determined using Zeeman-scanning techniques at kilogauss magnetic fields. The $m_J=-\frac{1}{2}$, $m_I=-\frac{7}{2}$ hyperfine Zeeman substate was populated selectively by irradiating the cesium-vapor-noble-gas mixture with cesium-resonance radiation, and collisional transitions to the $m_J=+\frac{1}{2}$, $m_I=-\frac{7}{2}$ substate were monitored by measurements of the relative intensities of the ${\sigma }^{-}$ and ${\sigma }^{+}$ components in resonance fluorescence observed in the direction parallel to the magnetic field. The following cross sections were obtained: Cs-He, 11.8 ${\mathrm{\AA }}^2$; Cs-Ne, 4.7 ${\mathrm{\AA }}^2$; Cs-Ar, 10.7 ${\mathrm{\AA }}^2$; Cs-Kr, 37.9 ${\mathrm{\AA }}^2$; Cs-Xe, 71.7 ${\mathrm{\AA }}^2$.

Charge-state fractions and yields of highly excited deuterium atoms produced by electron capture when 8-100-keV deuterons emerge from C, Mg, Nb, and Au surfaces deposited on thin carbon foils under high-vacuum conditions are reported. Atoms with principal quantum number $n=6\mathrm{}$ were detected with an optical technique; atoms in the levels $n\approx 12 \mathrm{to} 18$ were detected by ionizing them in a strong electric field. Changes with time after evaporation, presumably due to contamination of the surfaces, were observed. The experimental results are compared with available theoretical estimates. Solid and vapor targets are compared for Mg.

The "linear-model" parametric equation of state of Schofield, Litster, and Ho is used to analyze the effect of gravity near the gas-liquid critical point of a fluid. Detailed results are presented on the density distribution as a function of height, the constant-volume specific heat, and the low-frequency sound velocity, for arbitrary points in the ($\rho , T$) plane near the critical point. The influence of gravity on the determination of critical exponents is also considered. It is concluded that even for the thinnest practical samples, gravity corrections may have a significant effect on the exponents. The present theory permits gravity corrections to be made in a self-consistent way, with high accuracy.

Application is made of the reduced-density-matrix variational principle using a pair matrix constructed of geminals obtained from $1s$, $2s$, and $2p$ orbitals. The objective is to test the strength of the Pauli restriction on the 1 matrix and certain symmetry conditions for improving the lower bound to the ground-state energy. With the particular trial pair matrix used, the Pauli restriction on the 1 matrix improves the percentage error in the energy lower bound for ${\mathrm{C}}^{++}$ by a factor of approximately 6.

The unretarded London-van der Waals force between a neutral polarizable particle and a conducting wall, and between two neutral polarizable particles are derived from classical electromagnetism under the assumption that the universe contains fluctuating classical electromagnetic radiation with a Lorentz-invariant spectrum, (classical electromagnetic zero-point radiation). The classical derivations correspond in detail to the familiar charge-fluctuation arguments which have been advanced previously as qualitative semiclassical descriptions of quantum calculations of these forces.

The generalized Langevin approach of Mori is used to derive the relaxation matrix for a simple model system with internal degrees of freedom. The relationship between the damping matrix with a projected time dependence, and one with the usual time development is employed to compare the results obtained with those of Weinberg and Oppenheim. Furthermore, the conditions necessary to make a Markovian approximation are presented and discussed. Finally, a brief comparison is made with other works.

Necessary conditions for the absence of "runaways" are presented for electrons moving in a neutral gas under the influence of a steady-state uniform electric field. Then, simple and clarifying concepts are presented relevant to the comparison between the usual expression of the drift velocity and a recent expression given in a preceding paper in the framework of a path-integral formalism. For a steady-state uniform situation, the equivalence of the two definitions, recently questioned, is proved in very general conditions. In the Appendix, critical comments are introduced concerning the treatment of path-integral methods in a well-known book.

The entropy of mixing is calculated for two nonideal two-dimensional mixtures. System I consists of two different monomers with nearest-neighbor interactions between different monomers, and system II of monomers and tetramers without interactions. The entropies of mixing are evaluated exactly for strips of various heights. An extrapolation technique is introduced to obtain approximate results for infinite systems. In both cases the entropy of mixing is decreased compared to the ideal solution. For system I it remains symmetric with respect to the concentration $c=0.5\mathrm{}$ and shows a characteristic dip for sufficiently large interactions. The decrease in system II is asymmetric. It is much larger for high tetramer concentrations than for high monomer concentrations.

Measurements of the velocity of charge carriers in several dilute solutions of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in the temperature range 0.017-1.0 K are reported. The low-field negative-ion mobility shows a $T^{-\frac{1}{2}}$ dependence below 0.08 K characteristic of hard-sphere scattering. A maximum is observed in the mobility in the vicinity of 0.4 K. This can be interpreted in terms of a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ condensation on the bubble surface. The positive-ion mobility is nearly temperature independent below 0.7 K. This has recently been interpreted in terms of a momentum-dependent polarization scattering. The field dependence of the positive-carrier velocity shows a discontinuity in the vortex-ring regime. The discontinuity can be shown to result from a size-dependent drag coefficient and a maximum is observed for very small rings (∼16 Å).

The vanishing of certain coupling matrix elements at level crossings is shown to follow from angular momentum commutation relations. A magnetic dipole transition having $\Delta M=\pm 1$, induced near a crossing of the levels in a nonzero magnetic field, is found to have a dipole matrix element comparable to or smaller than the quotient of the level separation and the field. This result also applies in the analogous electric field electric dipole case.

The stability of electromagnetic waves propagating perpendicular to a uniform and static magnetic field is studied for plasmas with the ring- and loss-cone-type distributions in the perpendicular velocities. Based on the linearized Vlasov-Maxwell equations and the assumption that the ions are infinitely massive, it is found that instability can occur not only with zero frequency but also near the multiples of the electron cyclotron frequency. In general, the higher the average parallel energy, the more the plasma is susceptible to the instability. If the distribution in the parallel velocities is a stationary Maxwellian, instability occurs only for large ratios of parallel thermal pressure to magnetic pressure (${\beta }_{\parallel t}$). For counterstreaming plasmas with streaming velocities of the order of the electron thermal speed, the instability can occur for ${\beta }_{\parallel t}$ values of order unity. A discussion is given on the growth rates of these instabilities.

We present measurements of the specific heat $C_v$ of ${\mathrm{He}}^3$ with an impurity of 250-ppm ${\mathrm{He}}^4$ near its critical point, characterized by its density ${\rho }_c$ and temperature $T_c$. The sample cell had a vertical height of 0.5 mm to reduce the effect of gravity on the singularity. Data were taken along five isochores within the density range $-0.17<\Delta \rho <+0.11\mathrm{}$, where $\Delta \rho =\frac{(\rho -{\rho }_c)}{{\rho }_c}$, and in the temperature range $3\times {10}^{-5\mathrm{}}<\left|t\right|<{10}^{-1\mathrm{}}$, where $t=\frac{(T-T_c)}{T_c}$. The data are compared with previous $P-V-T$ measurements on this system and good consistency is shown between the two sets of data. An adequate description of the data along the critical isochore is found to be given by the extended scaling formulation of Green, Cooper, and Sengers, based on a generalized parametric equation of state. Within experimental error, the critical exponent describing the divergence of $C_v$ is the same for $t>\mathrm{}0\mathrm{}$ and $t<\mathrm{}0\mathrm{}$ and its value is $\alpha =0.105\mathrm{}\pm 0.015$. Scaled behavior of the specific heat as a function of temperature and density is exhibited by the data. This scaling is then related to the linear model of Schofield, Litster, and Ho. Good agreement is found between the calculated and the experimentally measured parameters for the linear model. Small systematic deviations will be discussed. We also present an account of the calorimeter relaxation times encountered in the vicinity of $T_c$. In the two-phase region, these relaxation times are much longer than in the one-phase region and diverge as the transition temperature is approached. This behavior is empirically described and tentatively attributed to processes at the boundary between the phases.

An investigation of superfluid-helium persistent currents in narrow annular channels is discussed, with an emphasis on the macroscopic linear superfluid velocity $v_s$. The channels have radial widths $d=R_2-R_1$ ranging from 8.20×${10}^{-1\mathrm{}}$ to 8.45×${10}^{-1\mathrm{}}$ cm, heights from 7.2 ×${10}^{-3\mathrm{}}$ to 4.6 cm, and contain no porous filler material. The observed maximum persistent velocities are identified as the superfluid critical velocity $v_{s,c}$ and constitute the first direct measurements of the linear superfluid critical velocity. These experimental values of $v_{s,c}$ are in fair agreement with a simple theory which intimately involves vortex lines. This theory includes a dissipative superfluid critical velocity involving pinned vortex lines which is in over-all agreement with the previous models of Feynman and of Glaberson and Donnelly, but which is especially appropriate for rotational experiments with our geometry. Also, the critical angular velocity of Donnelly and Fetter for the disappearance of vortex lines is associated with the superfluid rather than the bucket in the case of (metastable) persistent currents. Furthermore, it is shown that normal-fluid turbulence was avoided in these measurements and that, therefore, the criticism of Van Alphen et al. does not apply. Nevertheless, the present results do not agree with the empirical Leiden formula. Finally, Andronikashvili's original attempt to observe persistent currents is reexamined. The over-all results of this work strongly support the involvement of vortex lines in superfluid critical velocities for the cases investigated.

Collisional-excitation-rate coefficients for sodiumlike Ar viii ions have been obtained theoretically using the Coulomb-Born approximation as well as experimentally from the absolute intensities of lines emitted by these ions in well-diagnosed plasmas whose parameters were obtained from the analysis of scattered laser light. These plasmas were produced in a $\theta$-pinch device. The agreement between theory and experiment is within the estimated accuracy of ±50% for excitation from the ground state to the $n=3\mathrm{}$ and $n=4\mathrm{}$ levels, whereas some deviations are observed for two transitions to the $n=5\mathrm{}$ levels at lower temperatures. A rate coefficient for ionization was obtained from the time dependence of the ionization.

The radiative correction to the frequency of the spontaneous radiation from a system of two-level atoms in correlated states is calculated in the resonance approximation. A general prescription for renormalization without explicit reference to plane-wave states is given and used to obtain the renormalized frequency shifts. It is shown that the coherence frequency shift is not affected by the mass renormalization.

The correlation energy of the electron gas is studied for a characteristic range of metallic densities ($2<\mathrm{}{\mathcal{r}}_s<6\mathrm{}$) using a variational wave function of the form $\Psi =D\Pi {i<j}^{}\left[f\right({\mathcal{r}}_{\mathrm{ij}}\left)\right]$, where $D$ is a determinant of plane waves and spin functions and $f\left({\mathcal{r}}_{\mathrm{ij}}\right)$ is a correlation function of the form used by Becker et al. The problem is divided into two parts with the help of the method developed by Wu and Feenberg to take into account the antisymmetry of the wave function. First, the ground-state energy of the gas of charged bosons described by states of the form $\phi =\Pi {i<j}^{}\left[f\right({\mathcal{r}}_{\mathrm{ij}}\left)\right]$ is calculated by a Monte Carlo method for $0.5<\mathrm{}{\mathcal{r}}_s<20\mathrm{}$. The long-range correlations are taken into account by means of a lattice-summation technique already used by Brush et al. in their treatment of a classical one-component plasma. The resulting ground-state energies lie below the best existing results, and it is conjectured that the present values are an upper bound to the exact ground-state energy of a system of charged bosons. Assuming a zero-spin ground state for the metallic densities, the Wu-Feenberg expansion is then applied up to second order, allowing for two- and three-particle exchanges in the wave function. The resulting correlation energies are situated between the values obtained from the Nozières-Pines interpolation formula and those given by Singwi et al. in their dielectric approach. The corresponding pair-distribution functions are positive at all separations but do not satisfy the usual normalization condition. Higher-order exchanges in the wave function seem to be important and would tend to lower the correlation energy.